1/1*3+1/3*5+1/5*7...+1/99*101过程答案是什么?

Question

1/1*3+1/3*5+1/5*7...+1/99*101过程答案是什么?

Answer 1

1/1*3+1/3*5+1/5*7...+1/99*101
=1/2×[(1-1/3)+(1/3-1/5)+(1/5-1/7)+...+(1/99-1/101)]
=1/2×(1-1/101)
=1/2×100/101
=50/101